In the field of computation theory, concatenation is one of the regular operations. If A and B are languages (not necessarily regular languages) then the concatenation of A and B (usually written AB) is defined as follows.
{xy
| x ∈ A and y ∈ B}
In plain English: AB is the set of all strings which can be created by concatenating (read: putting together) a string from A with a string from B.
For example, if A = {yes,no}, and B = {maybe,probably}
AB = {yesmaybe,yesprobably,nomaybe,noprobably}
Some interesting things to note about the concatenation operation:
- Concatenation of strings and concatenation of languages are very different. Many fallacious proofs are based on this fact.
- Unlike the union operation, concatenation is not commutative. Unless A and B are equivalent, AB and BA are different languages.
- Regular languages are closed under the concatenation operation. This means that if A and B are regular languages, then so is AB.